Question

Integrating factor of linear differential equation $x\frac{dy}{dx}+2y=x^2\log x$ is ________.

• A. $\frac{1}{x^2}$
• B. $\frac{1}{x}$
• C. $x$
• D. $x^2$

Answer 1

The correct option is D $x^2$

Given $x\frac{dy}{dx}+2y=x^2\log x$

$\Rightarrow \frac{dy}{dx}+\frac{2}{x}y=x\log x$

Here $p=\frac{2}{x}$

Thus integrating factor $=e^{\int pdx}=e^{\int \frac{2}{x}dx}=e^{2\log x}=x^2$